6-5 Operations With Functions

1.

(2x + 5) - (x² + 3x - 2)         Distribute the -1.

(2x + 5) + (-x² - 3x + 2)       Now we can get rid of the parenthesees.

2x + 5 - x² - 3x + 2             Combine like terms.

-x² - x + 7                           Write in descending order.

2.

(x - 3)(x + 1)²                        Write out what the exponent means.

(x - 3)(x + 1)(x + 1)                Multiply each term in each set of parenthesees
(x² - 2x - 3)(x + 1)                 with each term in every other set.

x³ + x² - 2x² - 2x - 3x - 3     Combine like terms.

x³ - x² - 5x - 3

3.

(x² - x - 6) / (x² - 4)                      Factor the numerator and denominator.

[(x - 3)(x + 2)] / [(x - 2)(x + 2)]       The (x + 2)s cancel.

(x - 3) / (x - 2)